Pseudo-phase production simulation: a signal processing approach to assess quasi-multiphase flow production via successive analogous step-function relative permeability controlled models in reservoir flow simulation

ABSTRACT

The disclosed embodiments include a method, apparatus, and computer program product for approximating multiphase flow in reservoir simulation. For example, one disclosed embodiment includes a system that includes at least one processor and memory coupled to the at least one processor, the memory storing instructions that when executed by the at least one processor performs operations that includes generating a set of pseudo-phase production relative permeability curves; receiving production rate history data; receiving simulation configuration parameters; performing flow simulation using the set of pseudo-phase production relative permeability curves; and determining an optimal matching pseudo-phase production simulation result that best matches the production rate history data in the absence of relative permeability measurements derived from the subsurface porous medium.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a U.S. National Stage patent application ofInternational Patent Application No. PCT/US2013/059987, filed on Sep.16, 2013, the benefit of which is claimed and the disclosure of which isincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to the field of computerizedreservoir modeling, and more particularly, to a system and methodconfigured to approximate multiphase flow simulation using one or morepseudo-phase single flow relative permeability curves.

2. Discussion of the Related Art

Reservoir modeling and numerical simulation involving multiphase flows(i.e., flows where more than two phases (e.g., water and oil) arepresent) through a porous medium poses far greater challenges than thatof single-phase flows due in part to interfaces between phases. Due tothe overall complexity of multiphase flow simulation, the time needed tosimulate multiphase flows are substantially greater than its singlephase counterpart. In addition, simulation of multiphase flows requiresa greater understanding of fluid property characteristics to accuratelymodel the complex fluid system.

Accordingly, the disclosed embodiments seek to provide one or moresolutions for one or more of the above problems associated withreservoir modeling involving multiphase flows.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the present invention are described indetail below with reference to the attached drawing figures, which areincorporated by reference herein and wherein:

FIGS. 1A-1B depict a flowchart that illustrates an example of a processfor approximating multiphase flow in accordance with the disclosedembodiments;

FIG. 2 is a graph that depicts an example of a drainage oil-waterrelative permeability curve in accordance with the disclosedembodiments;

FIG. 3 is a graph that depicts an example of a relative permeabilityratio curve in accordance with the disclosed embodiments;

FIG. 4 is a graph that depicts an example of a step-functionsampling/pseudo-phase relative permeability curve in accordance with thedisclosed embodiments;

FIG. 5 is a graph that depicts an example of an oil-water relativepermeability curve that illustrates an underlying original relativepermeability being displayed with several pseudo-phase relativepermeability curves that were used in the pseudo-phase simulation toapproximate two phase flow through single “pseudo” phases in accordancewith the disclosed embodiments;

FIG. 6 is a graph that depicts an example of a historical oil productionrate curve shown relative to raw (non-interpolated) oil production rateplots resulting from disparate pseudo-phase simulation runs inaccordance with the disclosed embodiments;

FIG. 7 is a graph that depicts an example of a historical oil productionrate curve shown relative to time-interpolated oil production rate plotsresulting from disparate pseudo-phase simulation runs in accordance withthe disclosed embodiments;

FIG. 8 is a graph that depicts an example of the results of computedcorrelations of each pseudo-phase production oil rate curve relative tothe historical production in accordance with the disclosed embodiments;

FIG. 9 is a graph that depicts an example of the relative differencebetween individual pseudo-phase production oil rate results with respectto historical simulation data in accordance with the disclosedembodiments;

FIG. 10 is a graph that depicts an example of the relative error forvarying pseudo-phase production runs computed over simulated time inaccordance with the disclosed embodiments;

FIG. 11 is a graph that depicts an example of the cumulative error inpseudo-phase production oil rates relative to historical data over theentire simulated time in accordance with the disclosed embodiments;

FIG. 12 is a graph that depicts an example of a composite curvejuxtaposed with time-interpolated pseudo-phase production rate curvesand a historical production rate curve in accordance with the disclosedembodiments;

FIG. 13 is a graph that depicts an example of pseudo-phase productiontime-interpolated rate curves plotted with a variety of averagedpseudo-phase production rate curves derived from numerical and weighted(global and local) averaging techniques in accordance with the disclosedembodiments; and

FIG. 14 is a block diagram illustrating one embodiment of a system forimplementing the disclosed embodiments.

DETAILED DESCRIPTION

The disclosed embodiments include a system, computer program product,and a computer implemented method configured to perform a pseudo-phaseproduction simulation. Pseudo-phase as referenced herein meansapproximating two or more phase (i.e., multiphase) flow using a singlephase flow. A purpose of pseudo-phase production simulation is to extendthe application of single phase flow simulation as an efficient means ofpredicting actual multiphase reservoir production. Additionally, thedisclosed embodiments seek to treat relative permeability curves, whichare input into a reservoir simulator to describe fluid-fluid andfluid-rock interaction, as a synthesized signal to approximate differentflow regimes which may exist during production; then use thisapproximation to validate a given static model with respect toproduction history.

One advantage of the disclosed embodiments is that it would diminish runtimes as compared to the run times for performing multiphase flowproduction simulation. In addition, the disclosed embodiments decreasethe complexity and knowledge needed to provide a comparison of generalflow modeling relative to production history for the non-esoteric user.

The disclosed embodiments and additional advantages thereof are bestunderstood by referring to FIGS. 1A-14 of the drawings, like numeralsbeing used for like and corresponding parts of the various drawings.Other features and advantages of the disclosed embodiments will be orwill become apparent to one of ordinary skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional features and advantages be includedwithin the scope of the disclosed embodiments. Further, the illustratedfigures are only exemplary and are not intended to assert or imply anylimitation with regard to the environment, architecture, design, orprocess in which different embodiments may be implemented.

Beginning with FIG. 1A, an example of a computer implementedmethod/process 100 for approximating multiphase flow in accordance withthe disclosed embodiments is presented. The process 100 begins at step102 by importing/receiving one or more petrophysical rock models (alsocommonly referred to as earth models) and production history data. Inone embodiment, the earth models comprise three dimensional (3D)volumes/cells that include assigned values describing the physical andchemical rock properties and their interactions with fluid. For example,in one embodiment, the assigned values include a permeability value anda porosity value associated with the rock type. The earth models may begenerated using software such as, but not limited to, DecisionSpace®Earth Modeling software available from Landmark Graphics Corporation. Inone embodiment, multiple earth models are cosimulated (i.e., multiplerealizations of the earth model is generated with slightly differentproperty values, e.g., porosity and permeability values are differentfor each realization). In certain embodiments, the process 100 mayselect a particular realization that is determined to be most accuratebased on user-defined parameters and/or based on a comparison ofprevious production data then proceeds to simulation with the selectedrealization. In other embodiments, the process 100 may performsimulation on multiple realizations of the earth model.

As stated above, at step 102, the process 100 also receives productionhistory data such as, but not limited to, production rate data. Theamount of production history data may vary from several months toseveral years. In one embodiment, the reservoir production history datarepresents a time domain feature that is processed as a time dependentsignal with components of varying frequency for analyzing the timedomain data to determine the existence of flow regimes. Additionally, insome embodiments, the process is configured to identify thecomponentization of flow behavior according to spectral qualities thatexist in the resulting production during signal processing.

In addition, at step 104, the process 200 includes creating one or morepseudo-phase production relative permeability (K_(r)) curves thatdescribe fluid-fluid and fluid-rock interaction. Permeability is theability for fluids to flow in porous media. In multiphase flow, therelative permeability of a phase is a measure of dependent ratio ofeffective permeability of that phase to absolute permeability withrespect to an independent measure of saturation variation that varieswith time (K_(r)=K_(effective)/K_(absolute)).

An example of a relative permeability curve 200 is illustrated in FIG.2. In particular, the relative permeability curve 200 is a drainageoil-water relative permeability curve. While water saturation isexpressed as the independent axis, it is in fact a proxy for time. Thisis demonstrated in the Buckley-Leverett transport equation, which isused to model two-phase flow in porous media. The Buckley-Leverettequation is expressed as:

$\frac{\partial S}{\partial t} = {{U(S)}\frac{\partial S}{\partial x}}$where ${U(S)} = {\frac{Q}{\varphi\; A}\frac{df}{dS}}$

Here, S(x, t) is the water saturation, f is the fractional flow rate, Qis the total flow, φ is porosity and A is the area of the cross-sectionin the porous media.

The relative permeability curve 200 depicts a drainage two-phase systemwhere a non-wetting fluid (oil) phase displaces a present wetting(water) phase in the porous media. The porous medium is initiallysaturated with water and then via a displacement process triggered byinjection of an oil phase into the porous medium, the water saturation(i.e., the relative volume of water present) decreases as the volume ofoil increases. At the terminus of the relative permeability curve 200,water saturation is approximately 0.15 (or 15%), which is referred to asthe irreducible water saturation (or Swirr). Thus, relative permeabilitychanges with time due to changes in saturation of one fluid phaserelative to another. This relationship may expressed using the followingformula:S_(w)(t)→kr_(w,nw)(S_(w),t)where ‘S_(w)’ is water saturation, ‘kr’ is relative permeability, the‘w’ subscript refers to wetting fluid phase, the ‘nw’ subscript refersto non-wetting fluid phase, and ‘t’ is time.

A profile of water saturation with time is typically derivable from thecore/plug flooding experiment performed during special core analysis(SCAL or SPCAN) to generate the relative permeability curves. Specialcore analysis is a laboratory procedure for conducting flow experimentson core plugs taken from a petroleum reservoir. In particular, specialcore analysis includes measurements of two-phase flow properties,determining relative permeability, and capillary pressure andresistivity index using cores, slabs, sidewalls or plugs of a drilledwellbore. The derived relative permeability and capillary pressure actas input into a reservoir simulator to describe multiphase flow in thesubsurface porous media and allow the simulation of fluids in the mediawith the requisite purpose of matching simulation to historicalproduction data and forecasting future production. The process ofspecial core analysis has been known to take upwards of eighteen totwenty-four months and results are not typically guaranteed due toprocedural errors/inaccuracies as well as other risks associated withconducting invasive experiments on physical objects (cores, plugs,etc.).

Based on the above limitations associated with performing special coreanalysis, the disclosed embodiments provide an alternative method fordetermining a profile of relative permeability for a given rock type inthe absence of relative permeability being measured in acore/sidewall/plug (i.e., derived from special core analysis). Forinstance, the disclosed embodiments propose the use of a novel method,referred herein as pseudo-phase production, to approximate multiphaseflow using a single phase flow by sampling disparate instances ofrelative permeability at determined periods of stable fluid saturation.In particular, in one embodiment, a computer implemented method isdisclosed that approximates different instances of relativepermeability, for a given saturation, by simulating flow in a stagedapproach (i.e., flow one phase at a time while inhibiting the motion ofthe other phase)—hence creating a pseudo-phase simulation. In otherwords, two fluid phases would exist in the system, but only one fluidphase is in motion at a given instant.

In one embodiment, the disclosed embodiments utilize discrete,non-physical, relative permeability curves to approximate fluid flowusing a collection of step-function relative permeability curves (alsoreferred to herein as a pseudo-phase curves). The step-function relativepermeability curves represent flow of a single phase in the presence ofanother immobile fluid phase. The step-function relative permeabilitycurves have abrupt changes in relative permeability at a cross-overpoint where the mobile fluid becomes immobile and the initially immobilefluid becomes mobile (i.e., location in curve where ratio of relativepermeability (krw/krnw) is equal to 1). An example illustration of therelative permeability ratio (krw/krnw) for the curves in FIG. 2 is shownas a logarithmic plot in FIG. 3, where ‘w’ refers to the water phase,which is wetting, and ‘nw’ refers to the oil phase which is thenon-wetting phase.

In one embodiment, the step-function relative permeability curves arecreated in the form of an analog flow system. For instance, an examplestep-function sampling curve/pseudo-phase curve is illustrated in FIG.4.

In some embodiments, multiple step-function relative permeability curvesare generated with respective cross-over points occurring at varioussaturation intervals. The disclosed embodiments then uses the collectionof corresponding step-function relative permeability curves, withcross-over locations at varying points along the original relativepermeability curve to sample multiphase flow in a water-oil modeledsystem. For example, FIG. 5 illustrates selected sampling pseudo-phaserelative permeability curves (506-524) relative to an original relativepermeability curve (502 and 504). In the depicted embodiment, theillustrated pseudo-phase curves were used in the execution of subsequentsimulations; whereby each executed simulation uses each of thepseudo-phase curves respectively.

Referring back to FIG. 1A, once the pseudo-phase curves are generated,the process, at step 106, imports the pseudo-phase curves as asynthesized signal into a reservoir simulation application, such as, butnot limited to, Nexus® Reservoir Simulation software available fromLandmark Graphics Corporation, for performing flow simulation.Additionally, the process receives simulation configuration parameterssuch as, but not limited to, grid properties (e.g., grid cell size andtotal number of cells simulated), reservoir model type (e.g.,oil/water), simulated time period, number of producing wells and waterinjector wells along with rate and pressure constraints, initialPressure-Volume-Temperature (PVT) conditions, and phase contact depth.

Once the parameters are configured, the process performs pseudo-phasesimulation at step 108. In one embodiment, the process outputs theresulting oil production rate plots from the pseudo-phase modelsjuxtaposed with respect to the historical production. For example, FIG.6 illustrates the raw oil production rate results from the flowsimulations that are construed using KRW_ORG and KRO_ORG from FIG. 2 asthe sole input for relative permeability. The historical oil productionrate curve 602 is illustrated relative to raw (non-interpolated) oilproduction rate plots (604-616) resulting from disparate pseudo-phasesimulation runs. As depicted in FIG. 6, prior to 1000 days of cumulativesimulated time, the modeled reservoir remains in single phase depletiongiven the equivalence in oil production rate of the original(historical) run with respect to the resulting pseudo-phase generatedruns.

In some embodiments, the process at step 110 performs interpolation ofrate data in the time axis as necessary in order to compare pseudo-phaseresults to production history. Interpolation is a method of constructingnew data points within the range of a discrete set of known data pointsso that there is consistency among the results (e.g., result plots canbe adjusted to have the same number of data points, same time scale, andmeasurements at the same points in time). For instance, in contrast toFIG. 6, FIG. 7 shows time interpolated oil production rate plots suchthat all oil production rate plots have an identical discretization oftime. The historical oil production rate curve (702) is depictedrelative to time-interpolated oil production rate plots (704-716)resulting from disparate pseudo-phase simulation runs, which areillustrated as separate dotted lines. Similar to FIG. 6, prior to 1000days of cumulative time the modeled reservoir remains in single phasedepletion given the equivalence in oil production rate of the original(historical) run with respect to the resulting pseudo-phase generatedruns.

In order to assess the relationship of the position of the relativepermeability cross-over for each pseudo-phase production relativepermeability curves, the process at step 112 computes the correlationcoefficient of each pseudo-phase production oil rate curve relative tothe historical production. For example, in one embodiment, the processmay at step 114 may plot the pseudo-phase production correlation asshown in FIG. 8 to determine the best correlation. In the depictedexample, the pseudo-phase relative permeability curve with a cross-overat water saturation of 0.3 (labeled PSEUDOMULT13 in Table 1) has thegreatest correlation with the actual relative permeability curve.

TABLE 1 Pseudo-phase production correlation with respect to historicalproduction. Pseudo-Phase Production I.D. Correlation PSEUDOMULT12A0.5774 PSEUDOMULT11C 0.4438 PSEUDOMULT12 0.6631 PSEUDOMULT13 0.9306PSEUDOMULT13C 0.8461 PSEUDOMULT13D 0.8997

At step 116, the process then computes the relative error ofPseudo-Phase Production rate curves with respect to historical dataacross all simulated time to determine the difference between productionrates at given instances of time. In certain embodiments, the process,at step 118, may optionally generate a graph 900, as illustrated in FIG.9, that contrasts the pseudo-phase production curves (904-914) againsthistorical production (902), which has a relative error of “0” at everyinstance of time with respect to itself, and displayed with a computedminimization function (labeled Min. Function 916). The Min. Function 916describes the relative error of a construed composite curve derived fromhonoring a constructed objective function that seeks to minimize therelative error for all instances of simulation time for everyimplemented pseudo-phase curve. In addition, the Min. Function 916enables the determination of a best approximation of historical datausing the rates of minimum error from individual pseudo-phase productionrates.

Additionally, in certain embodiments, the process at step 124 maycalculate the area under each curve in FIG. 9 (e.g., using the TrapezoidRule) to determine the optimal pseudo-phase curve that best approximateshistorical production by the minimization of error in oil productionrate. In one embodiment, the process determines a total error as asingular value to identify the pseudo-phase production curve that hasminimum error with respect to the historical production rates. Forinstance, in some embodiments, the process may at step 126 generate oneor more graphs that plot relative error across simulated time and as acumulative value. For example, FIG. 10 shows the relative error as anerror plot for each pseudo-phase curve as a function of time, while FIG.11 shows the bar graphs for total calculated relative error acrosssimulated time for each pseudo-phase production scenario. As illustratedin FIGS. 10 and 11, in the depicted example, the smallest total errorover simulated time is 7.86 square units (occurring in runPSEUDOMULT12), while the second smallest total error is 9.62 squareunits (occurring in run PSEUDOMULT13).

At step 124, the process determines whether the difference between theoptimal pseudo-phase curve with respect to the historical productionrates determined in the previous steps (e.g., PSEUDOMULT12 illustratedin FIGS. 10 and 11) is within a user-defined error threshold. In otherwords, a user may define how large of an error may exist between thedetermined optimal pseudo-phase curve in comparison to the historicaldata. For instance, if the error between the optimal pseudo-phase curveand the historical production rates exceeds the user-defined errorthreshold, then a determination is made that there is no goodcorrelation between the pseudo-phase curves with respect to thehistorical production rates (i.e., the particular pseudo-phase runs donot approximate any instance of production from the particularreservoir). In one embodiment, if the error between the optimalpseudo-phase curve and the historical production rates exceeds theuser-defined error threshold, the process returns to step 104 andcreates new pseudo-phase production relative permeability curves andrepeats the process 100.

Referring to FIG. 1B, in one embodiment, if the error between theoptimal pseudo-phase curve with respect to the historical productionrates is within the user-defined error threshold, the process at step130 computes one or more of a composite, average, and weighted averagecurves that provide a description of production rate through the unionof pseudo-phase relative permeability curves. Additionally, the processmay at step 132 generate charts that plot the composite, average, and/orweighted average curves.

In one embodiment, the process creates the composite production ratecurve by modifying the basis curve, derived from optimizing curveselection based on relative error, and replacing production rates frommore suitable instances of hydrocarbon production rates from pseudoproduction rate profiles that have minimized error with respect tohistorical production rates. In one embodiment, to create the compositecurve, the process will begin by using points along a best matchingcurve and altering it using points along other curves that have a bettermatch. For instance, FIG. 12 provides an example composite curveillustrated with two disparate pseudo-phase production curves. Asdepicted in FIG. 12, while spikes in production rate are present thecomposite curve, it still represents a collectively better match tohistorical data compared to individual Pseudo-Phase Production ratecurves.

The average pseudo-phase production curve represents the numericalaveraging of a range of selected pseudo-phase production rate resultsacross simulated time. In certain embodiments, the process may createthe weighted-average production rate curves using global or localmethods; both respective methods are implemented by applying a discreteweighting factor to an intrinsic pseudo-phase production rate resultbefore normalization. The global method represents the bestapproximation of the entire production rate history over time, while thelocal method represents the best approximation of historical productionrate at more discrete time intervals. As an example, all averagingschemes (numerical, global weighted and local weighted) are illustratedin FIG. 13.

At step 134, the process determines the best overall match of the actualpseudo-phase production runs, composite(s), averages and weightedaverages with respect to production history. For these particular set ofpseudo-phase production runs, as shown in FIG. 13, the global and localweighted average curves possess a better match with respect tohistorical data than the non-weighted curves.

Accordingly, the disclosed embodiments provide an alternative method forperforming multiphase flow simulation that uses one or more pseudo-phasesingle flow relative permeability curves as a proxy for approximatingmultiphase flow simulation. As can be seen from the above process, thedisclosed embodiments provided at least one pseudo-phase production rateresult that sufficiently matched historical production data.Additionally, the disclosed embodiments may include deriving a compositerate curve that matched production rate to historical rate data atspecific time intervals and may also include deriving average ratecurves (numerical, globally weighted and locally weighted) that matchedproduction rate to historical data that are less apt to contain spikesin rate due to numerical smoothing associated with averaging data.

With reference to FIG. 14, a block diagram illustrating one embodimentof a system 1400 for implementing the features and functions of thedisclosed embodiments is presented. The system 1400 includes, amongother components, a processor 1410, main memory 1402, secondary storageunit 1404, an input/output interface module 1406, and a communicationinterface module 1408. The processor 1410 may be any type or any numberof single core or multi-core processors capable of executinginstructions for performing the features and functions of the disclosedembodiments.

The input/output interface module 1406 enables the system 1400 toreceive user input (e.g., from a keyboard and mouse) and outputinformation to one or more devices such as, but not limited to,printers, external data storage devices, and audio speakers. The system1400 may optionally include a separate display module 1412 to enableinformation to be displayed on an integrated or external display device.For instance, the display module 1412 may include instructions orhardware (e.g., a graphics card or chip) for providing enhancedgraphics, touchscreen, and/or multi-touch functionalities associatedwith one or more display devices. For example, in one embodiment, thedisplay module 1412 is a NVIDIA® QuadroFX type graphics card thatenables viewing and manipulating of three-dimensional objects.

Main memory 1402 is volatile memory that stores currently executinginstructions/data or instructions/data that are prefetched forexecution. The secondary storage unit 1404 is non-volatile memory forstoring persistent data. The secondary storage unit 1404 may be orinclude any type of data storage component such as a hard drive, a flashdrive, or a memory card. In one embodiment, the secondary storage unit1404 stores the computer executable code/instructions and other relevantdata for enabling a user to perform the features and functions of thedisclosed embodiments.

For example, in accordance with the disclosed embodiments, the secondarystorage unit 1404 may permanently store the executable code/instructionsof an algorithm 1420 for approximating multiphase flow reservoirproduction simulation as described above. The instructions associatedwith the algorithm 1420 are then loaded from the secondary storage unit1404 to main memory 1402 during execution by the processor 1410 forperforming the disclosed embodiments. In addition, the secondary storageunit 1404 may store other executable code/instructions and data 1422such as, but not limited to, a reservoir simulation application for usewith the disclosed embodiments.

The communication interface module 1408 enables the system 1400 tocommunicate with the communications network 1430. For example, thenetwork interface module 1408 may include a network interface cardand/or a wireless transceiver for enabling the system 1400 to send andreceive data through the communications network 1430 and/or directlywith other devices.

The communications network 1430 may be any type of network including acombination of one or more of the following networks: a wide areanetwork, a local area network, one or more private networks, theInternet, a telephone network such as the public switched telephonenetwork (PSTN), one or more cellular networks, and wireless datanetworks. The communications network 1430 may include a plurality ofnetwork nodes (not depicted) such as routers, network accesspoints/gateways, switches, DNS servers, proxy servers, and other networknodes for assisting in routing of data/communications between devices.

For example, in one embodiment, the system 1400 may interact with one ormore servers 1430 or databases 1432 for performing the features of thepresent invention. For instance, the system 1400 may query the database1432 for well log information in accordance with the disclosedembodiments. In one embodiment, the database 1432 may utilize OpenWorks®software available from Landmark Graphics Corporation to effectivelymanage, access, and analyze a broad range of oilfield project data in asingle database. Further, in certain embodiments, the system 1400 mayact as a server system for one or more client devices or a peer systemfor peer to peer communications or parallel processing with one or moredevices/computing systems (e.g., clusters, grids).

While specific details about the above embodiments have been described,the above hardware and software descriptions are intended merely asexample embodiments and are not intended to limit the structure orimplementation of the disclosed embodiments. For instance, although manyother internal components of the system 1400 are not shown, those ofordinary skill in the art will appreciate that such components and theirinterconnection are well known.

In addition, certain aspects of the disclosed embodiments, as outlinedabove, may be embodied in software that is executed using one or moreprocessing units/components. Program aspects of the technology may bethought of as “products” or “articles of manufacture” typically in theform of executable code and/or associated data that is carried on orembodied in a type of machine readable medium. Tangible non-transitory“storage” type media (i.e., a computer program product) include any orall of the memory or other storage for the computers, processors or thelike, or associated modules thereof, such as various semiconductormemories, tape drives, disk drives, optical or magnetic disks, and thelike, which may provide storage at any time for the softwareprogramming.

Additionally, the flowchart and block diagrams in the figures illustratethe architecture, functionality, and operation of possibleimplementations of systems, methods and computer program productsaccording to various embodiments of the present invention. It shouldalso be noted that, in some alternative implementations, the functions,instructions, or code noted in a block diagram or illustrated pseudocodemay occur out of the order noted in the figures. For example, two blocksshown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

Accordingly, the disclosed embodiments provide a system, computerprogram product, and method for approximating multiphase flow reservoirproduction simulation using a single pseudo-phase flow. In addition tothe embodiments described above, many examples of specific combinationsare within the scope of the disclosure, some of which are detailedbelow.

One example is a computer-implemented method, system, or anon-transitory computer readable medium for approximating multiphaseflow reservoir production simulation, that implements instructionscomprising: generating a set of pseudo-phase production relativepermeability curves; receiving production rate history data; receivingsimulation configuration parameters; performing flow simulation usingthe set of pseudo-phase production relative permeability curves; anddetermining an optimal matching pseudo-phase production simulationresult that best matches the production rate history data.

In certain embodiments, in determining an optimal matching pseudo-phaseproduction simulation result that best matches the production ratehistory data, the computer-implemented method, system, or non-transitorycomputer readable medium includes or implements instructions thatperforms at least one of computing a correlation coefficient for eachpseudo-phase production simulation result relative to the productionrate history data, and computing a relative error for each pseudo-phaseproduction simulation result relative to the production rate historydata across all simulated time to determine a difference betweenproduction rate at given instances of time for each pseudo-phaseproduction simulation result. In addition, in certain embodiments, thecomputer-implemented method, system, or non-transitory computer readablemedium includes or implements instructions that generates at least oneof a composite, average, and weighted average curve that provides adescription of production rate through a union of pseudo-phase relativepermeability curves.

The above specific example embodiments are not intended to limit thescope of the claims. For instance, the example embodiments may bemodified by including, excluding, or combining one or more features,steps, instructions, or functions described in the given example or inthe disclosure.

As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprise”and/or “comprising,” when used in this specification and/or the claims,specify the presence of stated features, integers, steps, operations,elements, and/or components, but do not preclude the presence oraddition of one or more other features, integers, steps, operations,elements, components, and/or groups thereof. The correspondingstructures, materials, acts, and equivalents of all means or step plusfunction elements in the claims below are intended to include anystructure, material, or act for performing the function in combinationwith other claimed elements as specifically claimed. The description ofthe present invention has been presented for purposes of illustrationand description, but is not intended to be exhaustive or limited to theinvention in the form disclosed. Many modifications and variations willbe apparent to those of ordinary skill in the art without departing fromthe scope and spirit of the invention. The embodiment was chosen anddescribed to explain the principles of the invention and the practicalapplication, and to enable others of ordinary skill in the art tounderstand the invention for various embodiments with variousmodifications as are suited to the particular use contemplated. Thescope of the claims is intended to broadly cover the disclosedembodiments and any such modification.

The invention claimed is:
 1. A computer-implemented method forapproximating multiphase flow in reservoir simulation, the methodcomprising: generating a set of pseudo-phase production relativepermeability curves representing a single phase of a multiphase fluidflow through a subsurface porous medium; receiving production ratehistory data; receiving simulation configuration parameters; performingflow simulation using each pseudo-phase production relative permeabilitycurve in the set of pseudo-phase production relative permeability curvesand the simulation configuration parameters; determining an optimalmatching pseudo-phase production simulation result that best matches theproduction rate history data, wherein the determination is made in theabsence of relative permeability measurements derived from thesubsurface porous medium and by: interpolating pseudo-phase productionrate data resulting from the flow simulation for each pseudo-phaseproduction relative permeability curve; comparing the interpolatedpseudo-phase production rate data for each pseudo-phase productionrelative permeability curve to the production rate history data; andselecting at least one of the pseudo-phase production relativepermeability curves as the optimal matching pseudo-phase productionsimulation result, based on the comparison; and approximating themultiphase fluid flow through the subsurface porous medium, based on theoptimal matching pseudo-phase production simulation result.
 2. Thecomputer-implemented method of claim 1, wherein determining an optimalmatching pseudo-phase production simulation result that best matches theproduction rate history data includes computing a correlationcoefficient for each pseudo-phase production simulation result relativeto the production rate history data.
 3. The computer-implemented methodof claim 1, wherein determining an optimal matching pseudo-phaseproduction simulation result that best matches the production ratehistory data includes computing a relative error for each pseudo-phaseproduction simulation result relative to the production rate historydata across all simulated time to determine a difference betweenproduction rate at given instances of time.
 4. The computer-implementedmethod of claim 1, wherein the set of pseudo-phase production relativepermeability curves is a set of step-function relative permeabilitycurves that represent flow of the single phase in the presence ofanother immobile fluid phase.
 5. The computer-implemented method ofclaim 4, wherein the set of step-function relative permeability curveshas cross-over locations at varying points along an original relativepermeability curve.
 6. The computer-implemented method of claim 1,wherein receiving simulation configuration parameters includes importingat least one petrophysical rock model.
 7. The computer-implementedmethod of claim 1, wherein determining an optimal matching pseudo-phaseproduction simulation result that best matches the production ratehistory data includes generating at least one of a composite, average,and weighted average curve that provides a description of productionrate through a union of pseudo-phase relative permeability curves; anddetermining whether the at least one of a composite, average, andweighted average curve provides the optimal matching pseudo-phaseproduction simulation result.
 8. The computer-implemented method ofclaim 7, wherein the weighted average curve is a global weighted averagecurve that applies a discrete weighting factor that provides arepresentation of a best approximation of an entire production ratehistory over time.
 9. The computer-implemented method of claim 7,wherein the weighted average curve is a local weighted average curvethat applies a discrete weighting factor that provides a representationof a best approximation of historical production rate at discrete timeintervals.
 10. A system, comprising: at least one processor; and atleast one memory coupled to the at least one processor and storingcomputer executable instructions for approximating multiphase flowreservoir production simulation, which, when executed by the at leastone processor, cause the at least one processor to perform operationscomprising: generating a set of pseudo-phase production relativepermeability curves representing a single phase of a multiphase fluidflow through a subsurface porous medium; receiving production ratehistory data; receiving simulation configuration parameters; performingflow simulation using each pseudo-phase production relative permeabilitycurve in the set of pseudo-phase production relative permeability curvesand the simulation configuration parameters; determining an optimalmatching pseudo-phase production simulation result that best matches theproduction rate history data by: interpolating pseudo-phase productionrate data resulting from the flow simulation for each pseudo-phaseproduction relative permeability curve; comparing the interpolatedpseudo-phase production rate data for each pseudo-phase productionrelative permeability curve to the production rate history data; andselecting at least one of the pseudo-phase production relativepermeability curves as the optimal matching pseudo-phase productionsimulation result, based on the comparison; and approximating themultiphase fluid flow through the subsurface porous medium, based on theoptimal matching pseudo-phase production simulation result.
 11. Thesystem of claim 10, wherein the instructions for determining an optimalmatching pseudo-phase production simulation result that best matches theproduction rate history data includes computing a correlationcoefficient for each pseudo-phase production simulation result relativeto the production rate history data.
 12. The system of claim 10, whereinthe instructions for determining an optimal matching pseudo-phaseproduction simulation result that best matches the production ratehistory data includes computing a relative error for each pseudo-phaseproduction simulation result relative to the production rate historydata across all simulated time to determine a difference betweenproduction rate at given instances of time.
 13. The system of claim 10,wherein the set of pseudo-phase production relative permeability curvesis a set of step-function relative permeability curves that representflow of the single phase in the presence of another immobile fluidphase, the set of step-function relative permeability curves havingcross-over locations at varying points along an original relativepermeability curve.
 14. The system of claim 10, wherein the instructionsfor determining an optimal matching pseudo-phase production simulationresult that best matches the production rate history data includesgenerating at least one of a composite, average, and weighted averagecurve that provides a description of production rate through a union ofpseudo-phase relative permeability curves; and determining whether theat least one of a composite, average, and weighted average curveprovides the optimal matching pseudo-phase production simulation result.15. The system of claim 14, wherein the weighted average curve is aglobal weighted average curve that applies a discrete weighting factorthat provides a representation of a best approximation of an entireproduction rate history over time.
 16. The system of claim 14, whereinthe weighted average curve is a local weighted average curve thatapplies a discrete weighting factor that provides a representation of abest approximation of historical production rate at discrete timeintervals.
 17. A non-transitory computer readable medium comprisingcomputer executable instructions for approximating multiphase flow inreservoir simulation, the computer executable instructions when executedcauses one or more machines to perform operations comprising: generatinga set of pseudo-phase production relative permeability curvesrepresenting a single phase of a multiphase fluid flow through asubsurface porous medium; receiving production rate history data;receiving simulation configuration parameters; performing flowsimulation using each pseudo-phase production relative permeabilitycurve in the set of pseudo-phase production relative permeability curvesand the simulation configuration parameters; determining an optimalmatching pseudo-phase production simulation result that best matches theproduction rate history data, wherein the determination is made in theabsence of relative permeability measurements derived from thesubsurface porous medium and by: interpolating pseudo-phase productionrate data resulting from the flow simulation for each pseudo-phaseproduction relative permeability curve; comparing the interpolatedpseudo-phase production rate data for each pseudo-phase productionrelative permeability curve to the production rate history data; andselecting at least one of the pseudo-phase production relativepermeability curves as the optimal matching pseudo-phase productionsimulation result, based on the comparison; and approximating themultiphase fluid flow through the subsurface porous medium, based on theoptimal matching pseudo-phase production simulation result.
 18. Thenon-transitory computer readable medium of claim 17, wherein thecomputer executable instructions when executed further causes one ormore machines to perform operations comprising computing a correlationcoefficient for each pseudo-phase production simulation result relativeto the production rate history data.
 19. The non-transitory computerreadable medium of claim 17, wherein the computer executableinstructions when executed further causes one or more machines toperform operations comprising computing a relative error for eachpseudo-phase production simulation result relative to the productionrate history data across all simulated time to determine a differencebetween production rate at given instances of time.
 20. Thenon-transitory computer readable medium of claim 17, wherein thecomputer executable instructions when executed further causes one ormore machines to perform operations comprising generating at least oneof a composite, average, and weighted average curve that provides adescription of production rate through a union of pseudo-phase relativepermeability curves; and determining whether the at least one of acomposite, average, and weighted average curve provides the optimalmatching pseudo-phase production simulation result.